[tuning-math] Re: Transformations of glumma
- From: Gene W Smith <genewardsmith@xxxxxxxx>
- To: tuning-math@xxxxxxxxxxxxxxx
- Date: Sat, 13 Jul 2002 22:30:20 -0700
I checked each of these 12 scales for intervals which were close to a
7-limit consonance by a comma less than 15 cents. All of them had at
least one such comma, and the 31-et covers all of the commas.
> reca1b2 := [1, 21/20, 35/32, 6/5, 5/4, 21/16, 35/24, 3/2, 49/32,
> 12/7,
> 7/4,
> 9/5];
126/125 ^ 1728/1715 = [10, 9, 7, -9, 17, -9]
"Small diesic" temperament covered by 27, 31 and 58
> reca1b3 := [1, 15/14, 35/32, 6/5, 5/4, 9/7, 35/24, 3/2, 25/16, 12/7,
> 7/4,
> 15
> /8];
1728/1715
> reca2b1 := [1, 25/24, 21/20, 35/32, 5/4, 21/16, 10/7, 35/24, 3/2,
> 49/32,
> 5/3
> , 7/4];
126/125
> reca2b3 := [1, 21/20, 15/14, 9/8, 5/4, 21/16, 10/7, 3/2, 5/3, 7/4,
> 25/14,
> 15
> /8];
126/125
> reca3b1 := [1, 49/48, 15/14, 35/32, 7/6, 5/4, 7/5, 35/24, 3/2, 25/16,
> 7/4,
> 15/8];
225/224
> reca3b2 := [1, 21/20, 15/14, 9/8, 7/6, 49/40, 5/4, 21/16, 7/5, 3/2,
> 7/4,
> 15/
> 8];
126/125 ^ 225/224 ^ 2401/2400 = 31-et
> reca1c2 := [1, 25/24, 35/32, 8/7, 6/5, 5/4, 10/7, 35/24, 3/2, 5/3,
> 12/7,
> 7/4
> ];
126/125 ^ 1728/1715, small diesic
> reca1c3 := [1, 49/48, 35/32, 7/6, 6/5, 5/4, 7/5, 35/24, 3/2, 8/5,
> 12/7,
> 7/4]
> ;
1728/1715
> reca2c1 := [1, 21/20, 8/7, 6/5, 5/4, 21/16, 10/7, 3/2, 5/3, 12/7,
> 7/4,
> 9/5];
1029/1024^126/125 = [9, 5, -3, -21, 30, -13]
"quartaminorthirds" covered by 31, 46 and 77
> reca2c3 := [1, 21/20, 7/6, 49/40, 5/4, 21/16, 4/3, 7/5, 10/7, 3/2,
> 5/3,
> 7/4]
> ;
2401/2400^126/125 = 126/125^1728/1715 = small diesic
> reca3c1 := [1, 15/14, 7/6, 6/5, 5/4, 9/7, 7/5, 3/2, 8/5, 12/7, 7/4,
> 15/8];
225/224
> reca3c2 := [1, 15/14, 7/6, 5/4, 4/3, 7/5, 10/7, 3/2, 5/3, 7/4, 25/14,
> 15/8];
126/125^225/224 = [1, 4, 10, 12 -13, 4]
meantone, covered by 19, 31, 43, 50, 74
------------------------ Yahoo! Groups Sponsor ---------------------~-->
Save on REALTOR Fees
http://us.click.yahoo.com/Xw80LD/h1ZEAA/Ey.GAA/wHYolB/TM
---------------------------------------------------------------------~->
To unsubscribe from this group, send an email to:
tuning-math-unsubscribe@xxxxxxxxxxxxxxx
Your use of Yahoo! Groups is subject to http://docs.yahoo.com/info/terms/
____________________________________________________________
To learn how to configure this list via e-mail (subscribe,
unsubscribe, etc.), send a message to listar@xxxxxxxxxxxxx
with the subject line "info tuning-math". Or visit the
website: < //www.freelists.org/list/tuning-math > .
Other related posts:
